$\int\sin^{2}x\cos^{4}x\;dx$=?

Question

İntegral $sin^{2}(x).cos^{4}(x)dx$=?

Answer 1

$$\int sin^2xcos^4xdx$$

$$=$$

$$\int \frac{1}{2}(1-cos2x)\left(\frac{1}{2}(1+cos2x)\right)^2dx$$

$$=$$

$$\frac{1}{8}\int (1-cos2x)(1+cos2x)^2dx$$

$$=$$

$$\frac{1}{8}\int (1-cos^22x)(1+cos2x)dx$$

$$=$$

$$\frac{1}{8}\int sin^22x(1+cos2x)dx$$

$$=$$

$$\frac{1}{8}\int sin^22xdx+\frac{1}{8}\int sin^2xcos2xdx$$

 Bundan sonrası kolay artık.